tricky math math question

thanks for those who try and work on it
Take a piece of cardboard measuring 7 by 15 inches. Cut congruent squares out of each corner of the cardboard and fold up the edges to form an opened-top box. What is the maximum volume of a box that you can create in this manner?

thanks for those who try and work on it
Take a piece of cardboard measuring 7 by 15 inches. Cut congruent squares out of each corner of the cardboard and fold up the edges to form an opened-top box. What is the maximum volume of a box that you can create in this manner?

I'll start you off.

obviously, this is an optimization problem in which we'd like to maximize the volume of a box. so the question is, what formula will give us the volume of the box for us to maximize? let's take this step by step

did you draw a diagram? (for related rates and optimization problems, ALWAYS draw a diagram if applicable--here, of course, it's applicable)

Let the side-length of the squares we cut out at each corner be

then we have what you see in the diagram below.

we know that the volume of the box will be given by:

can you tell the length, width and height of the box from the diagram? if you can, there's your formula to maximize!